Since I frequently head south during the winter to warm up in the Caribbean, these two airlines are frequently used. I try to stay faithful to rack up frequent flyer miles and have earned several flights, upgrades to first class and otherwise enjoyed some modest perks from frequent flyer programs.
We have accounts in both airlines and can't wait to combine miles for the next trip.
That said, as with any flight planning, you really need to check sources of flights. AA and US Airways are used after I have searched the major travel search engines (Hipmunk, Kayak etc.) if the flights are time conveniently and priced well. Some places you can't use your favorite airline (Iceland is a good example). And while I have used American to fly to Europe, Air Canada's schedule and price could not be beat one time.
The final point here is that these two airlines have different pricing depending on which site you are searching. So check both sites for prices!